Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pelagic 10 3.797497
mu_beta0_pelagic 1 3.499213
beta1_yellow 7 2.170014
beta0_yellow 4 2.039782
beta1_pelagic 10 1.925740
beta2_pelagic 9 1.791148
beta0_pH 20 1.658502
beta1_black 7 1.585711
tau_beta0_pelagic 1 1.442510
beta3_pH 27 1.420602
beta0_black 4 1.416738
mu_beta0_pH 4 1.406676
beta2_yellow 2 1.344024
parameter n badRhat_avg
sd_comp 1 1.330651
beta2_pH 11 1.308468
beta3_pelagic 9 1.292922
beta1_pH 29 1.283371
beta3_black 10 1.241165
beta3_yellow 8 1.228160
beta2_black 5 1.205425
mu_beta0_yellow 1 1.201170
beta_H 1 1.200883
tau_beta0_pH 4 1.175800
tau_beta0_yellow 1 1.164055
beta4_pelagic 1 1.130420
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
beta0_black 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0
beta0_pelagic 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1
beta0_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta0_yellow 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
beta1_black 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0
beta1_pelagic 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta1_yellow 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1
beta2_black 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0
beta2_pelagic 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1
beta2_pH 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0
beta2_yellow 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
beta3_black 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1
beta3_pelagic 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1
beta3_pH 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
beta3_yellow 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1
beta4_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pelagic 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
mu_beta0_yellow 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.165 0.068 -0.295 -0.166 -0.025
mu_bc_H[2] -0.120 0.037 -0.188 -0.121 -0.040
mu_bc_H[3] -0.456 0.067 -0.580 -0.457 -0.323
mu_bc_H[4] -1.153 0.204 -1.554 -1.155 -0.739
mu_bc_H[5] 0.563 0.675 -0.322 0.468 2.167
mu_bc_H[6] -2.261 0.320 -2.883 -2.268 -1.621
mu_bc_H[7] -0.480 0.113 -0.701 -0.479 -0.266
mu_bc_H[8] 0.113 0.351 -0.502 0.090 0.870
mu_bc_H[9] -0.336 0.138 -0.608 -0.337 -0.064
mu_bc_H[10] -0.128 0.065 -0.252 -0.129 0.006
mu_bc_H[11] -0.130 0.036 -0.200 -0.131 -0.062
mu_bc_H[12] -0.267 0.108 -0.503 -0.258 -0.066
mu_bc_H[13] -0.153 0.076 -0.303 -0.153 -0.004
mu_bc_H[14] -0.311 0.098 -0.511 -0.310 -0.127
mu_bc_H[15] -0.345 0.049 -0.438 -0.347 -0.249
mu_bc_H[16] -0.270 0.376 -0.893 -0.306 0.588
mu_bc_R[1] 1.445 1.332 -2.566 1.847 2.881
mu_bc_R[2] 0.548 1.732 -4.706 1.093 2.380
mu_bc_R[3] 0.935 1.337 -3.424 1.334 2.193
mu_bc_R[4] -1.651 3.484 -13.295 -0.443 1.338
mu_bc_R[5] 1.161 1.848 -2.744 1.227 4.516
mu_bc_R[6] -0.619 1.546 -4.666 -0.268 1.408
mu_bc_R[7] -0.746 4.737 -12.780 2.057 2.772
mu_bc_R[8] -1.367 4.935 -16.067 1.017 2.337
mu_bc_R[9] -1.539 5.858 -17.447 1.421 3.322
mu_bc_R[10] -5.191 10.735 -32.848 0.766 3.938
mu_bc_R[11] -2.139 1.399 -5.021 -1.974 0.112
mu_bc_R[12] -3.145 1.421 -6.055 -3.021 -0.720
mu_bc_R[13] -2.481 1.281 -5.231 -2.342 -0.404
mu_bc_R[14] -2.635 1.612 -6.315 -2.438 -0.205
mu_bc_R[15] -2.254 1.160 -4.729 -2.112 -0.408
mu_bc_R[16] -1.944 1.301 -4.763 -1.792 0.169
tau_pH[1] 260542.465 4032552.065 109.705 994.303 116270.175
tau_pH[2] 2.428 0.320 1.856 2.417 3.101
tau_pH[3] 2.744 0.422 1.991 2.727 3.654
tau_pH[4] 9.031 3.211 4.358 8.518 16.488
tau_pH[5] 4.999 1.390 2.669 4.876 7.972
beta0_pH[1,1] 1.765 1.525 -2.594 2.145 3.739
beta0_pH[2,1] 1.512 1.854 -3.904 2.009 3.773
beta0_pH[3,1] 1.894 1.563 -2.831 2.269 3.837
beta0_pH[4,1] 0.149 3.560 -11.797 1.334 3.388
beta0_pH[5,1] 1.246 2.054 -3.223 1.383 4.931
beta0_pH[6,1] 5.198 6.104 -0.302 3.535 23.897
beta0_pH[7,1] -0.350 6.320 -14.782 2.856 6.146
beta0_pH[8,1] -1.905 5.196 -17.032 0.426 2.702
beta0_pH[9,1] -1.694 6.605 -18.843 1.510 4.512
beta0_pH[10,1] -5.080 10.812 -32.766 0.775 4.377
beta0_pH[11,1] -3.244 1.357 -6.099 -3.103 -1.036
beta0_pH[12,1] -3.112 1.404 -6.017 -2.990 -0.684
beta0_pH[13,1] -3.062 1.276 -5.800 -2.927 -0.980
beta0_pH[14,1] -3.324 1.620 -7.032 -3.143 -0.906
beta0_pH[15,1] -3.053 1.188 -5.534 -2.948 -1.100
beta0_pH[16,1] -3.281 1.297 -6.038 -3.182 -1.144
beta0_pH[1,2] 2.439 0.253 1.971 2.430 2.943
beta0_pH[2,2] 2.574 0.368 1.774 2.613 3.165
beta0_pH[3,2] 2.435 0.302 1.872 2.426 3.078
beta0_pH[4,2] 2.385 0.327 1.740 2.387 2.958
beta0_pH[5,2] 4.014 1.216 1.997 3.900 6.688
beta0_pH[6,2] 3.046 0.280 2.437 3.077 3.465
beta0_pH[7,2] 1.950 0.206 1.567 1.961 2.278
beta0_pH[8,2] 2.834 0.297 2.384 2.859 3.183
beta0_pH[9,2] 3.294 0.369 2.205 3.354 3.793
beta0_pH[10,2] 3.669 0.347 2.608 3.723 4.117
beta0_pH[11,2] -5.097 0.301 -5.699 -5.088 -4.511
beta0_pH[12,2] -5.003 0.478 -6.073 -4.965 -4.162
beta0_pH[13,2] -4.812 0.427 -5.606 -4.821 -3.960
beta0_pH[14,2] -5.733 0.507 -6.796 -5.681 -4.866
beta0_pH[15,2] -4.400 0.362 -5.084 -4.408 -3.669
beta0_pH[16,2] -5.051 0.389 -5.826 -5.044 -4.290
beta0_pH[1,3] 1.276 0.317 0.474 1.320 1.743
beta0_pH[2,3] 1.663 0.539 0.457 1.712 2.417
beta0_pH[3,3] 1.793 0.650 0.298 1.832 2.682
beta0_pH[4,3] 1.928 0.745 0.386 1.880 3.076
beta0_pH[5,3] 0.221 1.616 -2.770 0.244 3.774
beta0_pH[6,3] -1.315 1.902 -6.317 -0.793 0.867
beta0_pH[7,3] -0.625 1.143 -2.622 -0.806 1.006
beta0_pH[8,3] 0.339 0.187 -0.021 0.336 0.718
beta0_pH[9,3] 0.013 0.380 -0.716 0.018 0.691
beta0_pH[10,3] 0.679 0.404 -0.317 0.729 1.280
beta0_pH[11,4] 2.060 0.341 1.351 2.073 2.718
beta0_pH[12,4] 2.097 0.532 0.749 2.121 2.968
beta0_pH[13,4] 1.764 0.358 0.999 1.777 2.318
beta0_pH[14,4] 1.977 0.363 1.203 2.058 2.517
beta0_pH[15,4] 1.710 0.366 0.995 1.749 2.323
beta0_pH[16,4] 1.899 0.252 1.422 1.895 2.326
beta0_pH[11,5] -0.848 0.223 -1.311 -0.843 -0.419
beta0_pH[12,5] -2.742 0.220 -3.160 -2.742 -2.293
beta0_pH[13,5] -0.274 0.210 -0.715 -0.268 0.113
beta0_pH[14,5] -1.266 0.191 -1.646 -1.266 -0.887
beta0_pH[15,5] -1.175 0.203 -1.577 -1.177 -0.781
beta0_pH[16,5] -0.727 0.193 -1.124 -0.724 -0.355
beta1_pH[1,1] 1.384 0.506 0.819 1.288 2.543
beta1_pH[2,1] 0.790 0.298 0.440 0.741 1.437
beta1_pH[3,1] 0.951 0.359 0.469 0.907 1.641
beta1_pH[4,1] 0.948 0.812 0.209 0.835 2.186
beta1_pH[5,1] 1.429 1.153 0.165 1.223 3.746
beta1_pH[6,1] 3.379 9.126 0.272 1.465 16.793
beta1_pH[7,1] 1.905 1.815 0.165 1.570 6.088
beta1_pH[8,1] 1.694 0.652 0.761 1.636 2.964
beta1_pH[9,1] 1.663 2.025 0.134 1.377 4.191
beta1_pH[10,1] 0.987 0.255 0.614 0.979 1.382
beta1_pH[11,1] 2.392 0.263 1.936 2.379 2.926
beta1_pH[12,1] 1.443 0.388 0.858 1.401 2.314
beta1_pH[13,1] 1.783 0.273 1.283 1.776 2.329
beta1_pH[14,1] 1.531 0.302 1.044 1.511 2.100
beta1_pH[15,1] 1.528 0.369 0.971 1.479 2.379
beta1_pH[16,1] 3.294 0.555 2.457 3.207 4.596
beta1_pH[1,2] 1.515 9.493 0.007 1.093 2.234
beta1_pH[2,2] 0.961 2.280 0.007 0.736 2.583
beta1_pH[3,2] 1.185 1.585 0.038 1.171 1.874
beta1_pH[4,2] 1.131 4.328 0.005 0.774 3.258
beta1_pH[5,2] 21.115 76.504 0.000 0.003 317.514
beta1_pH[6,2] 0.307 1.375 0.000 0.001 2.325
beta1_pH[7,2] 0.222 1.054 0.000 0.001 1.893
beta1_pH[8,2] 4.884 14.446 0.000 0.002 55.007
beta1_pH[9,2] 0.235 1.177 0.000 0.001 1.857
beta1_pH[10,2] 0.300 1.878 0.000 0.001 1.753
beta1_pH[11,2] 7.064 0.349 6.380 7.065 7.735
beta1_pH[12,2] 6.999 0.628 5.908 6.944 8.398
beta1_pH[13,2] 7.361 0.469 6.439 7.359 8.308
beta1_pH[14,2] 7.662 0.543 6.704 7.607 8.795
beta1_pH[15,2] 6.985 0.404 6.187 6.995 7.752
beta1_pH[16,2] 7.810 0.430 6.954 7.799 8.661
beta1_pH[1,3] 2.043 0.532 1.286 1.986 3.241
beta1_pH[2,3] 1.034 1.479 0.008 0.869 3.130
beta1_pH[3,3] 1.103 1.044 0.007 0.976 3.662
beta1_pH[4,3] 1.295 1.228 0.006 1.188 3.567
beta1_pH[5,3] 2.569 2.471 0.326 2.198 6.977
beta1_pH[6,3] 3.893 13.846 0.298 2.100 9.898
beta1_pH[7,3] 2.205 1.686 0.241 2.081 4.909
beta1_pH[8,3] 2.683 0.337 2.050 2.685 3.338
beta1_pH[9,3] 2.054 0.431 1.245 2.040 2.902
beta1_pH[10,3] 2.705 0.478 1.960 2.655 3.870
beta1_pH[11,4] 0.821 2.798 0.002 0.563 2.063
beta1_pH[12,4] 0.931 1.393 0.004 0.819 2.435
beta1_pH[13,4] 0.814 0.803 0.002 0.748 2.417
beta1_pH[14,4] 3.039 9.653 0.003 0.583 42.832
beta1_pH[15,4] 0.904 1.880 0.001 0.608 5.193
beta1_pH[16,4] 0.735 0.717 0.001 0.695 2.016
beta1_pH[11,5] 11.910 12.558 1.801 6.938 49.138
beta1_pH[12,5] 18.659 28.107 3.607 10.374 83.020
beta1_pH[13,5] 16.444 22.092 3.143 9.887 64.692
beta1_pH[14,5] 14.407 15.548 2.084 9.092 65.579
beta1_pH[15,5] 13.632 25.309 2.335 8.775 48.873
beta1_pH[16,5] 14.875 49.318 1.972 8.397 43.691
beta2_pH[1,1] 2.342 3.058 0.158 1.115 11.055
beta2_pH[2,1] 2.788 3.182 0.175 1.664 12.031
beta2_pH[3,1] 3.401 3.255 0.287 2.411 12.472
beta2_pH[4,1] 2.639 4.046 -5.448 1.867 12.542
beta2_pH[5,1] 3.216 3.947 -2.960 2.336 13.455
beta2_pH[6,1] 3.037 3.934 -3.710 2.191 11.983
beta2_pH[7,1] 2.608 4.296 -6.415 1.990 12.351
beta2_pH[8,1] 3.279 3.624 0.149 2.034 13.734
beta2_pH[9,1] 2.610 4.326 -7.088 2.045 12.559
beta2_pH[10,1] 3.275 3.311 0.323 2.183 12.234
beta2_pH[11,1] 0.721 0.204 0.437 0.688 1.209
beta2_pH[12,1] 0.743 0.804 0.140 0.559 2.598
beta2_pH[13,1] 0.587 0.442 0.229 0.493 1.504
beta2_pH[14,1] 1.084 0.930 0.256 0.838 3.453
beta2_pH[15,1] 0.492 0.480 0.125 0.385 1.501
beta2_pH[16,1] 0.311 0.097 0.158 0.300 0.524
beta2_pH[1,2] 3.313 4.607 -6.342 2.598 14.381
beta2_pH[2,2] -2.656 6.175 -16.317 -2.230 10.580
beta2_pH[3,2] -4.931 4.701 -17.162 -3.788 1.468
beta2_pH[4,2] -4.204 5.788 -17.180 -3.568 8.245
beta2_pH[5,2] -0.024 6.622 -14.087 -0.021 13.475
beta2_pH[6,2] -0.505 6.515 -13.785 -0.653 13.292
beta2_pH[7,2] -0.465 6.505 -13.465 -0.612 13.289
beta2_pH[8,2] -0.539 6.534 -14.013 -0.710 13.594
beta2_pH[9,2] -0.331 6.642 -13.989 -0.538 13.767
beta2_pH[10,2] -0.202 6.404 -13.137 -0.224 13.205
beta2_pH[11,2] -5.751 2.658 -13.660 -4.971 -2.649
beta2_pH[12,2] -2.224 1.792 -6.666 -1.463 -0.528
beta2_pH[13,2] -3.149 2.019 -8.467 -2.570 -1.221
beta2_pH[14,2] -4.098 1.969 -9.027 -3.640 -1.629
beta2_pH[15,2] -6.069 3.062 -14.665 -5.287 -2.557
beta2_pH[16,2] -6.418 3.058 -15.272 -5.668 -3.113
beta2_pH[1,3] 4.159 3.741 0.297 3.080 14.434
beta2_pH[2,3] 2.137 4.593 -8.695 1.771 12.946
beta2_pH[3,3] 0.573 5.421 -11.361 0.795 12.248
beta2_pH[4,3] 2.221 5.419 -9.453 1.961 14.142
beta2_pH[5,3] 3.498 6.015 -10.541 3.866 15.047
beta2_pH[6,3] 4.684 5.467 -7.142 4.521 16.115
beta2_pH[7,3] 5.191 5.045 -5.081 4.673 15.973
beta2_pH[8,3] 8.247 4.784 2.394 7.084 21.303
beta2_pH[9,3] 6.458 4.194 1.225 5.432 17.190
beta2_pH[10,3] 4.875 3.987 0.477 4.160 15.339
beta2_pH[11,4] -2.786 5.683 -15.224 -2.139 8.963
beta2_pH[12,4] -0.662 6.306 -14.417 -0.398 11.030
beta2_pH[13,4] 0.417 6.230 -14.117 1.181 12.363
beta2_pH[14,4] -1.962 6.446 -15.827 -1.260 11.058
beta2_pH[15,4] -0.669 7.507 -16.730 1.185 12.034
beta2_pH[16,4] 1.728 6.107 -13.170 2.211 12.978
beta2_pH[11,5] -2.583 1.937 -8.569 -1.985 -0.699
beta2_pH[12,5] -2.877 1.960 -8.049 -2.364 -0.858
beta2_pH[13,5] -2.674 1.639 -7.106 -2.224 -0.957
beta2_pH[14,5] -2.944 1.839 -8.056 -2.533 -1.057
beta2_pH[15,5] -2.922 1.729 -7.057 -2.477 -1.161
beta2_pH[16,5] -2.794 2.038 -8.033 -2.237 -0.727
beta3_pH[1,1] 34.226 2.330 30.802 34.039 39.389
beta3_pH[2,1] 36.418 2.041 33.839 36.140 40.971
beta3_pH[3,1] 33.510 3.338 29.700 33.704 36.350
beta3_pH[4,1] 39.423 14.663 22.697 38.912 55.853
beta3_pH[5,1] 40.051 24.877 8.610 38.856 81.249
beta3_pH[6,1] 38.284 48.878 9.362 32.226 121.967
beta3_pH[7,1] 34.929 42.617 5.644 27.411 98.584
beta3_pH[8,1] 32.483 8.318 28.101 32.034 37.269
beta3_pH[9,1] 44.748 116.508 6.816 28.242 126.193
beta3_pH[10,1] 34.068 2.605 28.486 34.735 36.583
beta3_pH[11,1] 30.002 0.497 28.962 30.018 30.939
beta3_pH[12,1] 31.355 2.561 27.246 31.094 36.705
beta3_pH[13,1] 34.126 1.278 31.767 34.059 36.861
beta3_pH[14,1] 30.789 1.189 28.201 30.815 32.978
beta3_pH[15,1] 33.206 2.162 29.471 32.974 38.128
beta3_pH[16,1] 33.406 1.231 30.618 33.501 35.564
beta3_pH[1,2] 42.074 21.214 3.351 40.778 88.383
beta3_pH[2,2] 47.164 93.002 0.951 37.396 121.085
beta3_pH[3,2] 43.122 26.484 16.536 41.939 46.034
beta3_pH[4,2] 48.273 58.712 3.892 41.641 145.897
beta3_pH[5,2] 160.710 411.493 0.123 32.141 1711.529
beta3_pH[6,2] 102.555 273.856 0.103 31.075 828.834
beta3_pH[7,2] 27.383 35.092 0.049 16.725 142.881
beta3_pH[8,2] 131.959 300.779 0.100 25.990 1217.610
beta3_pH[9,2] 185.621 510.977 0.111 36.043 1898.081
beta3_pH[10,2] 173.172 303.245 0.108 36.603 1058.028
beta3_pH[11,2] 43.353 0.144 43.114 43.338 43.664
beta3_pH[12,2] 43.064 0.283 42.415 43.099 43.568
beta3_pH[13,2] 43.822 0.173 43.447 43.840 44.131
beta3_pH[14,2] 43.280 0.150 43.045 43.264 43.619
beta3_pH[15,2] 43.418 0.169 43.130 43.403 43.772
beta3_pH[16,2] 43.479 0.163 43.177 43.474 43.799
beta3_pH[1,3] 39.900 1.001 37.223 40.015 41.390
beta3_pH[2,3] 36.558 54.893 0.621 32.288 104.709
beta3_pH[3,3] 42.319 35.871 0.918 33.773 158.269
beta3_pH[4,3] 38.570 89.816 0.416 26.730 109.070
beta3_pH[5,3] 44.547 61.979 12.690 34.024 121.541
beta3_pH[6,3] 45.629 39.154 15.854 38.254 108.880
beta3_pH[7,3] 38.305 33.759 19.811 28.412 110.761
beta3_pH[8,3] 41.494 0.225 41.082 41.497 41.911
beta3_pH[9,3] 33.722 0.499 32.886 33.727 34.729
beta3_pH[10,3] 35.866 0.741 33.728 36.031 36.869
beta3_pH[11,4] 171.659 449.981 0.422 41.966 1887.175
beta3_pH[12,4] 32.094 21.598 0.156 30.605 84.497
beta3_pH[13,4] 25.892 13.368 0.094 32.144 39.288
beta3_pH[14,4] 677.842 985.741 13.534 45.402 2852.286
beta3_pH[15,4] 33.424 33.296 0.150 31.130 140.220
beta3_pH[16,4] 29.355 12.534 0.165 34.407 48.650
beta3_pH[11,5] 39.675 0.780 38.086 39.718 41.159
beta3_pH[12,5] 38.162 1.230 35.587 38.220 40.524
beta3_pH[13,5] 40.207 0.788 38.358 40.319 41.474
beta3_pH[14,5] 39.189 0.787 37.446 39.230 40.646
beta3_pH[15,5] 40.115 0.583 38.897 40.171 41.086
beta3_pH[16,5] 38.462 1.408 35.340 38.609 40.823
beta0_pelagic[1] 1.360 0.719 -0.077 1.450 2.340
beta0_pelagic[2] 0.957 0.520 -0.206 1.035 1.659
beta0_pelagic[3] 0.158 0.372 -0.829 0.226 0.708
beta0_pelagic[4] 0.249 0.339 -0.467 0.275 0.910
beta0_pelagic[5] -4.593 2.424 -10.440 -4.331 1.131
beta0_pelagic[6] -0.936 2.480 -5.782 -0.034 1.627
beta0_pelagic[7] -0.357 2.797 -5.626 1.492 1.821
beta0_pelagic[8] -0.781 2.826 -6.374 1.320 1.933
beta0_pelagic[9] 0.237 3.113 -5.459 2.183 2.954
beta0_pelagic[10] -0.220 2.921 -5.544 0.682 2.748
beta0_pelagic[11] 0.007 0.489 -1.062 0.061 0.729
beta0_pelagic[12] 1.688 0.132 1.435 1.686 1.959
beta0_pelagic[13] 0.329 0.186 -0.088 0.344 0.651
beta0_pelagic[14] -0.057 0.260 -0.673 -0.034 0.371
beta0_pelagic[15] -0.239 0.132 -0.494 -0.238 0.021
beta0_pelagic[16] 0.348 0.218 -0.233 0.386 0.661
beta1_pelagic[1] 0.913 0.733 0.000 0.816 2.375
beta1_pelagic[2] 0.653 0.592 0.000 0.606 1.807
beta1_pelagic[3] 0.889 0.421 0.286 0.800 2.023
beta1_pelagic[4] 0.956 0.374 0.260 0.927 1.766
beta1_pelagic[5] 5.976 2.450 0.001 5.693 11.780
beta1_pelagic[6] 3.086 3.441 0.000 1.755 9.835
beta1_pelagic[7] 55.090 145.424 0.000 5.994 560.134
beta1_pelagic[8] 2.915 2.896 0.000 2.501 9.093
beta1_pelagic[9] 3.825 6.054 0.000 1.338 19.970
beta1_pelagic[10] 2.892 2.892 0.000 2.106 8.181
beta1_pelagic[11] 3.660 1.063 2.166 3.508 5.954
beta1_pelagic[12] 2.765 0.278 2.240 2.759 3.337
beta1_pelagic[13] 2.842 0.746 1.801 2.699 4.701
beta1_pelagic[14] 4.476 1.294 2.890 4.154 8.319
beta1_pelagic[15] 2.874 0.244 2.439 2.865 3.387
beta1_pelagic[16] 3.433 0.703 2.672 3.233 5.505
beta2_pelagic[1] 2.727 4.362 -6.244 2.028 13.353
beta2_pelagic[2] 2.248 4.375 -7.084 1.694 12.459
beta2_pelagic[3] 2.876 3.294 0.116 1.602 11.620
beta2_pelagic[4] 2.980 3.333 0.180 1.990 12.387
beta2_pelagic[5] -9.785 5.006 -21.422 -9.128 -2.709
beta2_pelagic[6] -0.449 6.362 -12.157 0.106 13.114
beta2_pelagic[7] -2.451 9.238 -18.773 -4.442 16.002
beta2_pelagic[8] -1.773 6.796 -16.699 -0.863 8.888
beta2_pelagic[9] 1.808 7.443 -14.250 1.909 16.315
beta2_pelagic[10] -1.202 8.095 -17.014 -1.490 15.478
beta2_pelagic[11] 1.691 2.997 0.106 0.245 10.573
beta2_pelagic[12] 5.830 3.595 1.596 4.888 15.330
beta2_pelagic[13] 0.848 1.618 0.207 0.481 3.663
beta2_pelagic[14] 0.320 0.132 0.154 0.299 0.633
beta2_pelagic[15] 6.141 3.284 1.762 5.741 14.299
beta2_pelagic[16] 4.567 3.886 0.241 4.169 13.613
beta3_pelagic[1] 22.958 19.709 1.729 21.477 63.319
beta3_pelagic[2] 32.663 57.382 2.266 21.395 128.736
beta3_pelagic[3] 29.079 5.538 21.131 29.074 41.547
beta3_pelagic[4] 25.434 2.758 21.356 25.521 30.943
beta3_pelagic[5] 45.994 6.626 31.615 46.528 46.923
beta3_pelagic[6] 31.636 41.838 2.402 25.062 140.100
beta3_pelagic[7] 21.455 12.776 17.543 20.207 35.381
beta3_pelagic[8] 38.908 67.322 1.328 21.228 138.421
beta3_pelagic[9] 29.329 26.791 3.808 20.160 96.410
beta3_pelagic[10] 36.754 43.514 1.225 32.929 140.116
beta3_pelagic[11] 41.965 1.898 37.521 42.336 45.310
beta3_pelagic[12] 43.447 0.232 43.036 43.434 43.878
beta3_pelagic[13] 42.758 1.377 40.201 42.628 45.938
beta3_pelagic[14] 42.792 1.895 39.550 42.615 47.823
beta3_pelagic[15] 43.211 0.214 42.742 43.208 43.650
beta3_pelagic[16] 43.193 0.581 41.851 43.234 44.330
mu_beta0_pelagic[1] 0.642 0.635 -0.530 0.625 1.888
mu_beta0_pelagic[2] -1.096 2.446 -5.521 -0.434 2.535
mu_beta0_pelagic[3] 0.337 0.405 -0.486 0.348 1.124
tau_beta0_pelagic[1] 10.284 29.223 0.145 1.993 85.743
tau_beta0_pelagic[2] 8.289 29.118 0.019 0.236 80.585
tau_beta0_pelagic[3] 1.912 1.342 0.297 1.585 5.322
beta0_yellow[1] -0.551 0.219 -1.103 -0.522 -0.225
beta0_yellow[2] 0.509 0.149 0.209 0.511 0.792
beta0_yellow[3] -0.290 0.167 -0.620 -0.286 0.025
beta0_yellow[4] 0.809 0.255 0.090 0.851 1.162
beta0_yellow[5] -1.102 0.459 -2.013 -1.098 -0.198
beta0_yellow[6] 0.551 0.453 -0.085 0.398 1.369
beta0_yellow[7] 0.355 0.864 -1.574 0.791 1.303
beta0_yellow[8] 0.598 0.682 -1.146 0.898 1.265
beta0_yellow[9] -0.028 0.284 -0.524 -0.046 0.657
beta0_yellow[10] 0.238 0.152 -0.074 0.241 0.538
beta0_yellow[11] -2.357 0.702 -3.912 -2.274 -1.238
beta0_yellow[12] -3.563 0.428 -4.453 -3.542 -2.789
beta0_yellow[13] -3.740 0.490 -4.725 -3.728 -2.871
beta0_yellow[14] -2.388 0.589 -3.705 -2.378 -1.238
beta0_yellow[15] -2.900 0.436 -3.792 -2.870 -2.099
beta0_yellow[16] -2.574 0.492 -3.651 -2.560 -1.682
beta1_yellow[1] 0.565 0.774 0.000 0.460 1.808
beta1_yellow[2] 0.996 0.246 0.563 0.982 1.498
beta1_yellow[3] 0.651 0.253 0.130 0.650 1.101
beta1_yellow[4] 1.382 0.877 0.624 1.155 4.332
beta1_yellow[5] 3.049 3.018 0.002 2.635 9.738
beta1_yellow[6] 1.508 1.089 0.000 2.029 2.840
beta1_yellow[7] 1.158 1.314 0.000 1.073 3.549
beta1_yellow[8] 1.271 1.435 0.000 1.054 4.868
beta1_yellow[9] 1.478 1.552 0.005 1.449 2.145
beta1_yellow[10] 2.543 0.465 1.703 2.526 3.484
beta1_yellow[11] 2.481 0.696 1.406 2.382 4.058
beta1_yellow[12] 2.367 0.449 1.543 2.344 3.296
beta1_yellow[13] 2.941 0.489 2.077 2.921 3.935
beta1_yellow[14] 2.421 0.594 1.272 2.409 3.708
beta1_yellow[15] 2.187 0.434 1.370 2.153 3.048
beta1_yellow[16] 2.379 0.495 1.463 2.358 3.460
beta2_yellow[1] -3.409 4.790 -15.508 -2.872 5.879
beta2_yellow[2] -4.055 3.381 -13.220 -3.191 -0.331
beta2_yellow[3] -4.385 4.049 -15.306 -3.315 -0.177
beta2_yellow[4] -3.515 3.684 -13.416 -2.404 -0.100
beta2_yellow[5] -6.641 5.393 -19.467 -5.783 -0.321
beta2_yellow[6] 3.826 6.725 -11.894 3.955 16.976
beta2_yellow[7] 1.195 7.649 -15.102 1.597 16.193
beta2_yellow[8] -2.096 7.439 -16.489 -2.139 14.302
beta2_yellow[9] 6.368 5.024 -2.366 5.625 18.227
beta2_yellow[10] -7.390 4.865 -19.660 -6.329 -1.280
beta2_yellow[11] -3.697 2.751 -11.433 -2.968 -0.806
beta2_yellow[12] -4.121 2.722 -11.549 -3.396 -1.119
beta2_yellow[13] -4.245 2.661 -11.615 -3.498 -1.414
beta2_yellow[14] -4.263 3.015 -12.290 -3.472 -0.654
beta2_yellow[15] -3.803 2.775 -11.360 -3.063 -0.941
beta2_yellow[16] -4.385 2.933 -12.255 -3.571 -1.159
beta3_yellow[1] 35.703 85.338 7.092 28.945 63.624
beta3_yellow[2] 29.311 1.494 27.320 28.905 32.903
beta3_yellow[3] 33.725 7.476 29.130 32.878 39.919
beta3_yellow[4] 29.431 3.780 20.414 28.442 35.690
beta3_yellow[5] 33.835 7.050 27.653 33.421 37.868
beta3_yellow[6] 38.023 10.714 16.422 39.416 54.884
beta3_yellow[7] 34.289 20.759 12.834 29.050 76.311
beta3_yellow[8] 37.492 32.940 12.673 30.014 87.082
beta3_yellow[9] 37.741 9.175 32.728 37.536 42.151
beta3_yellow[10] 29.427 0.382 28.519 29.464 29.984
beta3_yellow[11] 45.787 0.819 44.271 45.792 47.251
beta3_yellow[12] 43.405 0.461 42.567 43.360 44.375
beta3_yellow[13] 44.838 0.378 44.014 44.903 45.475
beta3_yellow[14] 45.034 2.094 43.260 44.504 50.205
beta3_yellow[15] 45.288 0.623 44.156 45.259 46.426
beta3_yellow[16] 44.744 1.081 43.477 44.662 46.466
mu_beta0_yellow[1] 0.118 0.457 -0.806 0.118 1.050
mu_beta0_yellow[2] 0.097 0.458 -0.802 0.091 1.003
mu_beta0_yellow[3] -2.720 0.560 -3.738 -2.742 -1.421
tau_beta0_yellow[1] 2.643 2.995 0.197 1.837 9.731
tau_beta0_yellow[2] 2.715 8.198 0.256 1.466 10.746
tau_beta0_yellow[3] 4.405 12.823 0.193 1.726 27.987
beta0_black[1] 0.023 0.194 -0.327 0.015 0.402
beta0_black[2] 1.758 0.387 0.499 1.858 2.123
beta0_black[3] 1.237 0.264 0.407 1.285 1.555
beta0_black[4] 2.175 0.275 1.659 2.183 2.614
beta0_black[5] 1.599 1.574 -1.220 1.654 4.057
beta0_black[6] 1.599 1.599 -1.480 1.667 4.233
beta0_black[7] 1.618 1.445 -1.398 1.660 4.328
beta0_black[8] 1.294 0.217 0.860 1.292 1.716
beta0_black[9] 2.361 0.289 1.745 2.378 2.871
beta0_black[10] 1.470 0.128 1.220 1.472 1.714
beta0_black[11] 3.112 0.707 0.906 3.353 3.690
beta0_black[12] 4.487 0.189 4.113 4.485 4.848
beta0_black[13] -0.075 0.206 -0.491 -0.072 0.315
beta0_black[14] 2.122 0.516 0.809 2.232 2.747
beta0_black[15] 0.945 0.596 -0.914 1.133 1.517
beta0_black[16] 3.416 1.171 0.568 3.920 4.506
beta2_black[1] 3.399 5.818 -10.191 3.275 15.248
beta2_black[2] -0.296 6.018 -11.911 -0.845 13.390
beta2_black[3] -0.894 7.617 -18.613 0.225 12.923
beta2_black[4] -3.732 6.895 -18.667 -3.038 10.582
beta2_black[5] 0.012 6.261 -12.403 -0.253 13.583
beta2_black[6] -0.195 6.309 -13.482 -0.198 13.064
beta2_black[7] -0.156 6.409 -13.535 -0.293 13.229
beta2_black[8] -0.374 6.226 -13.249 -0.589 12.913
beta2_black[9] -0.170 6.386 -13.403 -0.264 12.822
beta2_black[10] -0.351 5.406 -10.047 -0.801 11.649
beta2_black[11] -0.980 4.339 -8.624 -1.470 12.075
beta2_black[12] -4.079 3.165 -12.834 -3.193 -0.752
beta2_black[13] -3.130 3.119 -12.370 -2.112 -0.520
beta2_black[14] -2.444 3.226 -11.747 -1.264 -0.118
beta2_black[15] -2.254 4.176 -12.489 -1.755 6.365
beta2_black[16] -2.301 4.478 -13.974 -1.787 4.983
beta3_black[1] 174.470 803.424 1.001 41.839 1433.814
beta3_black[2] 63.627 199.362 0.271 32.009 345.513
beta3_black[3] 114.164 379.438 0.447 34.740 1056.502
beta3_black[4] 63.046 156.348 0.514 32.780 456.184
beta3_black[5] 8829.619 233216.385 0.103 32.685 8550.490
beta3_black[6] 191798.969 8536126.983 0.180 33.678 14050.544
beta3_black[7] 10662.417 254550.930 0.090 31.655 7122.041
beta3_black[8] 115.002 282.325 0.106 28.264 952.215
beta3_black[9] 135.902 374.684 0.094 28.113 1199.285
beta3_black[10] 71.055 127.394 0.052 26.480 476.145
beta3_black[11] 38.599 26.498 13.878 32.655 110.643
beta3_black[12] 32.996 0.982 31.469 33.060 33.952
beta3_black[13] 39.303 0.648 37.735 39.379 40.424
beta3_black[14] 38.505 4.008 30.294 38.840 45.888
beta3_black[15] 35.938 21.311 11.167 34.135 69.158
beta3_black[16] 42.022 57.071 12.591 34.911 99.728
beta4_black[1] -0.276 0.185 -0.634 -0.277 0.092
beta4_black[2] 0.256 0.177 -0.092 0.256 0.610
beta4_black[3] -0.936 0.181 -1.289 -0.933 -0.574
beta4_black[4] 0.500 0.227 0.074 0.496 0.939
beta4_black[5] 0.247 2.502 -5.073 0.145 5.300
beta4_black[6] 0.263 2.724 -4.819 0.191 5.183
beta4_black[7] 0.273 2.450 -4.467 0.172 5.418
beta4_black[8] -0.725 0.357 -1.409 -0.726 -0.053
beta4_black[9] 1.522 1.038 -0.053 1.380 3.952
beta4_black[10] 0.024 0.179 -0.333 0.029 0.374
beta4_black[11] -0.689 0.206 -1.091 -0.686 -0.284
beta4_black[12] 0.309 0.329 -0.309 0.303 0.972
beta4_black[13] -1.199 0.210 -1.601 -1.198 -0.794
beta4_black[14] -0.120 0.231 -0.570 -0.123 0.337
beta4_black[15] -0.892 0.205 -1.309 -0.892 -0.501
beta4_black[16] -0.601 0.226 -1.055 -0.597 -0.161
mu_beta0_black[1] 1.220 0.750 -0.397 1.259 2.624
mu_beta0_black[2] 1.630 0.673 0.231 1.655 2.820
mu_beta0_black[3] 2.157 0.953 0.115 2.195 3.920
tau_beta0_black[1] 1.111 0.975 0.066 0.850 3.680
tau_beta0_black[2] 4.670 11.812 0.092 2.042 23.217
tau_beta0_black[3] 0.324 0.212 0.052 0.280 0.857
beta0_dsr[11] -2.902 0.279 -3.447 -2.905 -2.345
beta0_dsr[12] 4.353 1.006 3.728 4.491 5.007
beta0_dsr[13] -1.374 0.294 -1.985 -1.369 -0.837
beta0_dsr[14] -3.698 0.503 -4.704 -3.702 -2.721
beta0_dsr[15] -1.969 0.262 -2.501 -1.971 -1.458
beta0_dsr[16] -3.022 0.348 -3.700 -3.018 -2.353
beta1_dsr[11] 4.822 0.294 4.249 4.826 5.413
beta1_dsr[12] 5.989 4.850 2.267 5.034 15.431
beta1_dsr[13] 2.843 0.330 2.277 2.826 3.492
beta1_dsr[14] 6.346 0.529 5.308 6.338 7.409
beta1_dsr[15] 3.304 0.267 2.781 3.303 3.827
beta1_dsr[16] 5.821 0.364 5.136 5.812 6.545
beta2_dsr[11] -9.911 4.211 -20.246 -9.040 -4.669
beta2_dsr[12] -7.028 3.905 -16.650 -5.899 -2.270
beta2_dsr[13] -6.675 3.789 -15.150 -5.917 -1.175
beta2_dsr[14] -5.632 3.157 -12.972 -4.919 -1.655
beta2_dsr[15] -9.078 3.948 -19.721 -8.263 -3.943
beta2_dsr[16] -9.517 4.226 -20.644 -8.500 -4.310
beta3_dsr[11] 43.490 0.158 43.197 43.486 43.787
beta3_dsr[12] 34.462 2.757 32.575 34.186 35.000
beta3_dsr[13] 43.240 0.291 42.797 43.190 43.846
beta3_dsr[14] 43.365 0.227 43.073 43.317 43.907
beta3_dsr[15] 43.509 0.189 43.165 43.503 43.857
beta3_dsr[16] 43.443 0.171 43.155 43.429 43.787
beta4_dsr[11] 0.594 0.206 0.187 0.592 1.011
beta4_dsr[12] 0.276 0.443 -0.596 0.277 1.160
beta4_dsr[13] -0.138 0.205 -0.555 -0.140 0.261
beta4_dsr[14] 0.172 0.241 -0.314 0.174 0.631
beta4_dsr[15] 0.778 0.208 0.368 0.775 1.213
beta4_dsr[16] 0.155 0.226 -0.287 0.155 0.584
beta0_slope[11] -1.959 0.157 -2.271 -1.957 -1.656
beta0_slope[12] -4.598 0.221 -4.964 -4.611 -4.126
beta0_slope[13] -1.522 0.304 -2.299 -1.468 -1.115
beta0_slope[14] -2.673 0.173 -3.031 -2.671 -2.345
beta0_slope[15] -1.457 0.156 -1.765 -1.459 -1.156
beta0_slope[16] -2.762 0.169 -3.100 -2.764 -2.413
beta1_slope[11] 4.600 0.283 4.039 4.603 5.149
beta1_slope[12] 4.997 0.521 3.982 4.977 6.016
beta1_slope[13] 3.141 0.728 2.303 2.954 5.183
beta1_slope[14] 6.568 0.537 5.560 6.563 7.645
beta1_slope[15] 3.086 0.275 2.522 3.084 3.623
beta1_slope[16] 5.395 0.383 4.675 5.383 6.152
beta2_slope[11] 8.245 3.094 4.382 7.748 16.964
beta2_slope[12] 5.631 3.203 1.578 5.041 14.019
beta2_slope[13] 3.484 2.893 0.254 2.772 10.431
beta2_slope[14] 4.881 2.558 1.982 4.222 10.986
beta2_slope[15] 7.630 3.812 3.632 6.500 17.654
beta2_slope[16] 7.936 3.390 3.572 7.192 16.739
beta3_slope[11] 43.414 0.123 43.200 43.406 43.693
beta3_slope[12] 43.339 0.146 43.067 43.338 43.631
beta3_slope[13] 43.407 0.197 43.059 43.391 43.861
beta3_slope[14] 43.370 0.134 43.131 43.365 43.647
beta3_slope[15] 43.417 0.140 43.167 43.410 43.721
beta3_slope[16] 43.403 0.127 43.176 43.397 43.685
beta4_slope[11] -0.561 0.210 -0.973 -0.562 -0.153
beta4_slope[12] -1.517 0.686 -3.048 -1.423 -0.401
beta4_slope[13] 0.125 0.211 -0.286 0.124 0.543
beta4_slope[14] -0.158 0.255 -0.632 -0.161 0.369
beta4_slope[15] -0.661 0.205 -1.065 -0.660 -0.276
beta4_slope[16] -0.160 0.227 -0.596 -0.162 0.300
sigma_H[1] 0.220 0.047 0.134 0.218 0.319
sigma_H[2] 0.176 0.028 0.127 0.174 0.238
sigma_H[3] 0.186 0.041 0.112 0.184 0.273
sigma_H[4] 0.306 0.084 0.179 0.294 0.494
sigma_H[5] 0.950 0.220 0.544 0.939 1.404
sigma_H[6] 0.328 0.187 0.024 0.315 0.734
sigma_H[7] 0.290 0.055 0.202 0.282 0.417
sigma_H[8] 0.325 0.127 0.099 0.333 0.563
sigma_H[9] 0.486 0.123 0.303 0.467 0.780
sigma_H[10] 0.209 0.043 0.137 0.205 0.304
sigma_H[11] 0.274 0.046 0.197 0.270 0.374
sigma_H[12] 0.420 0.165 0.200 0.384 0.761
sigma_H[13] 0.221 0.037 0.157 0.218 0.301
sigma_H[14] 0.503 0.090 0.350 0.496 0.689
sigma_H[15] 0.251 0.039 0.185 0.247 0.337
sigma_H[16] 0.227 0.043 0.156 0.222 0.324
lambda_H[1] 3.388 4.590 0.171 1.865 16.527
lambda_H[2] 9.586 8.973 0.963 7.200 33.361
lambda_H[3] 6.301 8.979 0.328 3.566 26.994
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 1.575 3.602 0.015 0.367 12.188
lambda_H[6] 6.391 14.528 0.007 0.276 49.190
lambda_H[7] 0.016 0.011 0.003 0.014 0.047
lambda_H[8] 6.444 9.786 0.077 3.096 31.422
lambda_H[9] 0.018 0.012 0.003 0.014 0.048
lambda_H[10] 0.422 1.172 0.041 0.244 1.491
lambda_H[11] 0.259 0.522 0.011 0.112 1.217
lambda_H[12] 4.902 6.438 0.220 2.813 22.325
lambda_H[13] 3.571 3.367 0.219 2.647 11.955
lambda_H[14] 3.349 3.815 0.244 2.146 13.680
lambda_H[15] 0.024 0.030 0.003 0.016 0.090
lambda_H[16] 0.804 1.061 0.050 0.462 3.626
mu_lambda_H[1] 4.436 1.897 1.323 4.272 8.552
mu_lambda_H[2] 3.537 1.976 0.423 3.369 7.773
mu_lambda_H[3] 3.532 1.860 0.847 3.257 7.880
sigma_lambda_H[1] 8.789 4.224 2.163 8.214 17.983
sigma_lambda_H[2] 7.664 4.650 0.665 7.001 17.865
sigma_lambda_H[3] 6.361 3.968 1.142 5.561 16.015
beta_H[1,1] 6.942 1.012 4.540 7.081 8.562
beta_H[2,1] 9.890 0.447 8.955 9.915 10.695
beta_H[3,1] 8.004 0.701 6.337 8.099 9.160
beta_H[4,1] 9.835 7.634 -5.571 10.020 24.370
beta_H[5,1] -0.060 2.983 -5.916 -0.014 5.745
beta_H[6,1] 2.714 4.284 -7.672 4.050 8.019
beta_H[7,1] 2.107 5.165 -9.360 2.517 11.737
beta_H[8,1] 1.228 4.043 -2.822 1.090 3.727
beta_H[9,1] 13.836 5.639 2.868 13.627 25.485
beta_H[10,1] 7.139 1.586 3.890 7.195 10.111
beta_H[11,1] 4.783 3.653 -3.206 5.452 9.959
beta_H[12,1] 2.591 1.013 0.763 2.545 4.810
beta_H[13,1] 9.026 0.968 6.948 9.109 10.507
beta_H[14,1] 2.150 1.032 -0.025 2.179 4.082
beta_H[15,1] -6.296 3.769 -13.203 -6.471 1.869
beta_H[16,1] 3.298 2.612 -0.892 2.956 9.336
beta_H[1,2] 7.926 0.245 7.431 7.935 8.386
beta_H[2,2] 10.040 0.130 9.780 10.042 10.289
beta_H[3,2] 8.967 0.189 8.591 8.971 9.349
beta_H[4,2] 3.610 1.433 0.853 3.548 6.487
beta_H[5,2] 1.929 1.008 -0.053 1.920 3.876
beta_H[6,2] 5.701 1.159 3.102 5.874 7.461
beta_H[7,2] 2.141 1.010 0.346 2.055 4.259
beta_H[8,2] 2.974 1.171 1.087 3.118 4.379
beta_H[9,2] 3.041 1.086 0.944 3.033 5.184
beta_H[10,2] 8.197 0.328 7.517 8.206 8.829
beta_H[11,2] 9.837 0.656 8.852 9.726 11.263
beta_H[12,2] 3.956 0.360 3.284 3.947 4.680
beta_H[13,2] 9.149 0.265 8.692 9.126 9.693
beta_H[14,2] 4.026 0.348 3.327 4.026 4.704
beta_H[15,2] 11.403 0.673 9.988 11.432 12.620
beta_H[16,2] 4.472 0.794 2.981 4.464 6.078
beta_H[1,3] 8.546 0.233 8.127 8.532 9.032
beta_H[2,3] 10.106 0.107 9.895 10.106 10.317
beta_H[3,3] 9.667 0.157 9.370 9.660 9.999
beta_H[4,3] -2.259 0.855 -3.935 -2.261 -0.599
beta_H[5,3] 4.121 0.695 2.633 4.162 5.433
beta_H[6,3] 8.416 1.263 6.589 8.123 10.952
beta_H[7,3] -2.186 0.696 -3.609 -2.152 -0.909
beta_H[8,3] 5.482 0.576 4.728 5.386 6.691
beta_H[9,3] -2.168 0.782 -3.713 -2.162 -0.683
beta_H[10,3] 8.732 0.261 8.249 8.723 9.261
beta_H[11,3] 8.519 0.291 7.892 8.543 9.024
beta_H[12,3] 5.287 0.314 4.545 5.327 5.794
beta_H[13,3] 8.841 0.175 8.469 8.852 9.158
beta_H[14,3] 5.758 0.261 5.178 5.777 6.224
beta_H[15,3] 10.340 0.314 9.735 10.336 10.986
beta_H[16,3] 6.318 0.557 5.088 6.380 7.257
beta_H[1,4] 8.347 0.180 7.965 8.360 8.665
beta_H[2,4] 10.191 0.107 9.963 10.195 10.390
beta_H[3,4] 10.165 0.158 9.822 10.176 10.442
beta_H[4,4] 12.200 0.483 11.205 12.222 13.070
beta_H[5,4] 6.137 0.883 4.700 6.062 8.118
beta_H[6,4] 7.102 0.965 5.011 7.360 8.487
beta_H[7,4] 8.092 0.335 7.437 8.094 8.754
beta_H[8,4] 6.912 0.352 6.342 6.883 7.640
beta_H[9,4] 7.054 0.449 6.218 7.036 7.959
beta_H[10,4] 7.870 0.240 7.423 7.859 8.379
beta_H[11,4] 9.422 0.203 9.032 9.421 9.819
beta_H[12,4] 7.162 0.209 6.759 7.153 7.594
beta_H[13,4] 9.087 0.144 8.798 9.087 9.362
beta_H[14,4] 7.746 0.213 7.317 7.746 8.173
beta_H[15,4] 9.491 0.237 9.022 9.492 9.956
beta_H[16,4] 9.354 0.228 8.931 9.345 9.811
beta_H[1,5] 9.004 0.149 8.709 9.005 9.286
beta_H[2,5] 10.789 0.092 10.612 10.789 10.981
beta_H[3,5] 10.916 0.158 10.639 10.908 11.246
beta_H[4,5] 8.474 0.380 7.685 8.480 9.216
beta_H[5,5] 5.229 0.742 3.532 5.342 6.439
beta_H[6,5] 8.924 0.652 7.986 8.794 10.392
beta_H[7,5] 6.860 0.317 6.254 6.852 7.479
beta_H[8,5] 8.254 0.202 7.919 8.243 8.644
beta_H[9,5] 8.257 0.455 7.301 8.262 9.128
beta_H[10,5] 10.001 0.219 9.539 10.012 10.422
beta_H[11,5] 11.495 0.228 11.044 11.503 11.941
beta_H[12,5] 8.486 0.192 8.098 8.485 8.872
beta_H[13,5] 10.034 0.134 9.773 10.033 10.305
beta_H[14,5] 9.192 0.231 8.754 9.180 9.665
beta_H[15,5] 11.164 0.248 10.679 11.163 11.641
beta_H[16,5] 9.907 0.177 9.559 9.914 10.236
beta_H[1,6] 10.149 0.190 9.813 10.132 10.574
beta_H[2,6] 11.504 0.105 11.300 11.501 11.712
beta_H[3,6] 10.811 0.152 10.468 10.820 11.084
beta_H[4,6] 12.752 0.653 11.458 12.762 14.057
beta_H[5,6] 5.979 0.672 4.769 5.960 7.411
beta_H[6,6] 8.622 0.718 6.701 8.781 9.625
beta_H[7,6] 9.736 0.531 8.711 9.734 10.775
beta_H[8,6] 9.463 0.273 8.932 9.474 9.906
beta_H[9,6] 8.387 0.740 6.957 8.368 9.917
beta_H[10,6] 9.576 0.288 8.970 9.597 10.078
beta_H[11,6] 10.841 0.352 10.096 10.865 11.458
beta_H[12,6] 9.367 0.247 8.896 9.357 9.890
beta_H[13,6] 11.047 0.169 10.753 11.037 11.405
beta_H[14,6] 9.822 0.291 9.246 9.832 10.366
beta_H[15,6] 10.838 0.436 9.991 10.840 11.702
beta_H[16,6] 10.547 0.240 10.057 10.560 10.992
beta_H[1,7] 10.882 0.824 8.916 10.958 12.315
beta_H[2,7] 12.169 0.419 11.330 12.169 13.014
beta_H[3,7] 10.540 0.625 9.133 10.597 11.581
beta_H[4,7] 2.933 3.318 -3.742 2.899 9.365
beta_H[5,7] 6.732 2.481 2.590 6.521 12.416
beta_H[6,7] 9.669 2.663 4.713 9.389 16.749
beta_H[7,7] 11.008 2.700 5.905 10.941 16.508
beta_H[8,7] 10.957 1.090 9.381 10.866 13.069
beta_H[9,7] 4.737 3.836 -2.890 4.749 12.319
beta_H[10,7] 9.666 1.312 7.260 9.582 12.609
beta_H[11,7] 11.034 1.722 7.890 10.928 14.798
beta_H[12,7] 9.966 0.908 7.981 10.021 11.620
beta_H[13,7] 11.637 0.802 9.669 11.740 12.854
beta_H[14,7] 10.433 0.944 8.513 10.489 12.118
beta_H[15,7] 12.015 2.277 7.430 12.004 16.554
beta_H[16,7] 12.269 1.266 10.175 12.110 15.174
beta0_H[1] 8.429 13.121 -17.277 8.666 33.658
beta0_H[2] 10.668 5.710 -0.904 10.681 22.194
beta0_H[3] 10.042 9.416 -8.740 10.026 29.542
beta0_H[4] 5.229 190.573 -374.564 1.539 403.764
beta0_H[5] 5.767 36.561 -67.303 4.706 81.607
beta0_H[6] 7.534 56.601 -111.578 7.788 133.546
beta0_H[7] 5.060 119.352 -237.412 4.122 246.912
beta0_H[8] 6.267 35.859 -21.967 6.735 33.960
beta0_H[9] 4.528 113.400 -229.146 4.380 233.321
beta0_H[10] 9.351 30.209 -48.993 8.695 69.119
beta0_H[11] 7.120 52.083 -108.652 9.411 108.905
beta0_H[12] 6.776 10.687 -13.648 6.721 29.441
beta0_H[13] 9.517 13.946 -12.354 9.646 31.700
beta0_H[14] 6.973 11.146 -16.211 6.921 28.716
beta0_H[15] 12.188 109.820 -203.235 9.959 241.156
beta0_H[16] 8.157 23.798 -37.782 8.119 56.325